2nd/10_Wiki/Topics/Domain_Programming/AI_and_ML/Replenishment.md

id, title, category, status, canonical_id, aliases, duplicate_of, source_trust_level, confidence_score, verification_status, tags, raw_sources, last_reinforced, github_commit, tech_stack

id	title	category	status	canonical_id	aliases	duplicate_of	source_trust_level	confidence_score	verification_status	tags	raw_sources	last_reinforced	github_commit	tech_stack
wiki-2026-0508-replenishment	Replenishment	10_Wiki/Topics	verified	self	Inventory Replenishment Stock Replenishment 재고보충	none	A	0.9	applied	supply-chain inventory operations forecasting optimization		2026-05-10	pending	language framework Python pandas/scipy/forecasting

Replenishment

매 한 줄

"매 right item, right quantity, right time.". Replenishment 매 inventory 가 demand 의 동안 stockout 의 X 의 process 의 maintaining. 1934 Wilson EOQ 부터 modern AI-driven probabilistic forecasting (Amazon, Walmart 의 LSTM/Transformer demand models) 까지 evolved.

매 핵심

매 핵심 levers

• Reorder Point (ROP): trigger threshold = lead_time_demand + safety_stock.
• Order Quantity: how much (EOQ, min-max, fixed).
• Review period: continuous (Q-system) 의 X periodic (P-system).
• Safety Stock: buffer 의 demand/lead-time variability 의.

매 modern signals

• Probabilistic demand forecast (quantiles, 의 X point estimate).
• Lead time variance (supplier reliability score).
• Cross-location pooling (omnichannel inventory).
• Substitution + promotion lift modeling.

매 응용

1. Retail (Walmart, Costco 의 daily auto-replenishment).
2. E-commerce FBA (Amazon 의 fulfillment center distribution).
3. Manufacturing MRP (BOM-driven component replenishment).
4. Healthcare (vaccine, drug 의 cold-chain replenishment).

💻 패턴

EOQ (Economic Order Quantity)

import math

def eoq(annual_demand: float, order_cost: float, holding_cost_per_unit: float) -> float:
    """Wilson formula. Min total cost = order + holding."""
    return math.sqrt(2 * annual_demand * order_cost / holding_cost_per_unit)

# Example: 10K units/yr, $50/order, $2/unit/yr holding
print(eoq(10_000, 50, 2))  # 707 units per order

Reorder Point with Safety Stock

from scipy.stats import norm

def reorder_point(daily_demand_mean, daily_demand_std,
                  lead_time_days, service_level=0.95):
    z = norm.ppf(service_level)
    lead_time_demand = daily_demand_mean * lead_time_days
    safety_stock = z * daily_demand_std * math.sqrt(lead_time_days)
    return lead_time_demand + safety_stock, safety_stock

Min-Max (s, S) Policy

def min_max_order(on_hand: int, on_order: int, s: int, S: int) -> int:
    """매 inventory_position <= s 일 때 S 까지 order."""
    inv_pos = on_hand + on_order
    return max(0, S - inv_pos) if inv_pos <= s else 0

Probabilistic Forecast → Newsvendor

import numpy as np

def newsvendor_quantile(unit_cost, sale_price, salvage=0):
    """Critical ratio = (p - c) / (p - s)."""
    return (sale_price - unit_cost) / (sale_price - salvage)

def order_qty_from_forecast(demand_samples: np.ndarray, critical_ratio: float):
    return float(np.quantile(demand_samples, critical_ratio))

# 1000 Monte Carlo demand samples → optimal order
samples = np.random.gamma(shape=4, scale=25, size=1000)
cr = newsvendor_quantile(unit_cost=10, sale_price=25, salvage=3)
print(order_qty_from_forecast(samples, cr))

LSTM Demand Forecast (modern)

import torch.nn as nn

class DemandLSTM(nn.Module):
    def __init__(self, n_features=8, hidden=64):
        super().__init__()
        self.lstm = nn.LSTM(n_features, hidden, num_layers=2,
                            dropout=0.2, batch_first=True)
        self.head = nn.Linear(hidden, 3)  # P10, P50, P90 quantiles

    def forward(self, x):
        out, _ = self.lstm(x)
        return self.head(out[:, -1])

Multi-Echelon Allocation

def fair_share_allocation(forecasts: dict, total_supply: float) -> dict:
    """Allocate constrained supply across stores proportional to forecast."""
    total_demand = sum(forecasts.values())
    if total_supply >= total_demand:
        return forecasts.copy()
    ratio = total_supply / total_demand
    return {loc: f * ratio for loc, f in forecasts.items()}

KPI Dashboard

def replenishment_kpis(history: list[dict]) -> dict:
    stockouts = sum(1 for d in history if d["on_hand"] == 0)
    fill_rate = sum(d["fulfilled"] for d in history) / sum(d["demanded"] for d in history)
    avg_inv = sum(d["on_hand"] for d in history) / len(history)
    return {
        "service_level": 1 - stockouts / len(history),
        "fill_rate": fill_rate,
        "avg_inventory": avg_inv,
        "inventory_turns": sum(d["demanded"] for d in history) / avg_inv,
    }

매 결정 기준

상황	Approach
Stable demand, known lead time	EOQ + ROP
Highly variable demand	Probabilistic forecast + newsvendor
Many SKUs, low value	Min-Max (s, S)
Perishable / fashion	Newsvendor (single-period)
Multi-location, constrained supply	Fair-share / DRP
Modern e-commerce scale	ML demand model + RL ordering policy

기본값: Probabilistic LSTM forecast → newsvendor quantile order. 매 P50 forecast + ROP 의 단순 baseline 의 X.

🔗 Graph

• 부모: Supply Chain Management · Operations Research
• Adjacent: Reinforcement Learning · MRP

🤖 LLM 활용

언제: SKU master data 의 cleansing, supplier email parsing, anomaly explanation, what-if scenario 의 narrative. 언제 X: 매 actual demand forecasting 의 LLM 의 X — purpose-built time-series models (Prophet, NeuralForecast, Chronos) 의 use.

❌ 안티패턴

• Point forecast only: P50 만 사용 의 X — quantiles 의 사용 의 service level tuning 의 가능.
• Static safety stock: lead time 의 variance 의 ignore 의 X.
• Local optimization: 각 store 의 independent ordering — pooling 의 lost.
• Bullwhip ignored: downstream order 의 upstream 의 amplification 의 monitor 의 필요.
• Excel-only: 1000+ SKU 의 manual review 의 scale 의 X.

🧪 검증 / 중복

• Verified (Silver/Pyke "Inventory Management" textbook, AWS Forecast docs).
• 신뢰도 A.

🕓 Changelog

날짜	변경
2026-05-08	Phase 1
2026-05-10	Manual cleanup — replenishment policy + ML forecasting patterns